Question

Could you check this for me?

Answer 1

Explain how you would find the product of 2012 and 208. Include either the exponent rule or the expanded method in your explanation. Give your answer in exponential form.

If you wanted to find the product of 20^12. You could expand it 20 x 20 x 20 x 20 x 20 x 20 x 20 x 20 x 20 x 20 20 x 20 x 20 x 20 x 20 = 4.096 x 10^15(I put it in scientific notation because the number is huge)

208 = 25600000000.

The product would be, 25600000000 x 4.096 x 10^15 = 1.048576 x10^26

Answer 2

2012*208=(2000+12)(200+8)=2000*200+2000*8+12*200+12*8
=400000+1600+2400+96
calculate

Answer 3

Do you mean \(20^{12} \times 20^8\)? If so, I would use the exponent rules.

Answer 4

If you don't remember the exponent rules, then consider expanded form:
\((x \times x \times x \times x \times x \times x \times x \times x \times x \times x \times x \times x) \times (x \times x\times x\times x\times x\times x\times x\times x)\)
How many times are you multiplying 20?
An answer in exponent form is not the same as scientific notation.

Answer 5

i failed to understand how 2012=20^12

Answer 6

it may be 2012=2*10^3
208=2.1*10^2
product can be4.2*10^(3+2)=4.2*10^5

Answer 7

@phi is what i have correct?

Answer 8

if you mean explain \( 20^{12} \cdot 20^8 \)
Include either the exponent rule or the expanded method

the expanded method is almost what you did: write out 12 20's multiplied together. then multiply those by 8 20's multiplied together...
count the number of 20's and you get 12+8= 20 20's multiplies together, or
\( 20^{20} \)

the exponent rule is : for numbers with the same base (20 here), add the exponents if you are multiplying:
\[ 20^{12} \cdot 20^8= 20^{12+8} = 20^{20} \]

I don't think they want you to find the actual product, which is huge

Answer 9

they say
Give your answer in exponential form.

so 20^20 is what they want